The HCF of 28 and 56 is 28. The highest number that divides the given numbers exactly, without leaving a remainder, is termed as Highest Common Factor (HCF). In Mathematics, it is essential to learn the concepts and understand the basics thoroughly. For this purpose, BYJU’S expert teachers have formulated the article HCF. This article plays a vital role in clearing the doubts of students immediately and makes the learning HCF concept hassle-free. Let us learn the simple technique of how to determine the Highest Common Factor of 28 and 56 in a clear format in this article.
What is the HCF of 28 and 56?
The Highest Common Factor of 28 and 56 is 28. There are six common factors of 28 and 56. They are 1, 2, 4, 7, 14 and 28. Among these factors of 28 and 56, the largest number is 28. Hence, the Highest Common Factor of 28 and 56 is 28.
How to Find HCF of 28 and 56?
The following are the three methods used to find the HCF of 28 and 56:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 28 and 56 by Prime Factorisation Method
To determine the HCF using prime factorisation, we write the numbers as the product of prime factors. Hence, the numbers 28 and 56 can be written as shown below:
28 = 2 × 2 × 7
56 = 2 × 2 × 2 × 7
The common factors of 28 and 56 are 2, 2 and 7.
Therefore,
HCF (28, 56) = 2 × 2 × 7 = 28
HCF of 28 and 56 by Long Division Method
In the long division method, we use the following steps to find the Highest Common Factor of 28 and 56
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not 0, then make it a new divisor and write the previous divisor as the new dividend. Then continue the division process.
Step 3: Continue this process until we get the remainder equal to zero. The last divisor will be the HCF of the given two numbers.
The Highest Common Factor of 28 and 56 by the long division method is shown below:
HCF (28, 56) = 28
HCF of 28 and 56 by Listing Common Factors
In this method, to calculate the HCF, we list out all the factors of 28 and 56. The factors of 28 and 56 are as follows:
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Therefore, HCF (28, 56) = 28
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Solved Example
Question: What is the highest number that divides both 28 and 56 exactly?
Solution: The highest number that divides both 28 and 56 is their Highest Common Factor. To find the HCF, we need to list the factors of 28 and 56.
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Here, the Highest Common Factor of 28 and 56 is 28. Hence, the highest number that divides both 28 and 56 exactly is 28.
Frequently Asked Questions on HCF of 28 and 56
What is the HCF of 28 and 56?
What are the common factors of 28 and 56?
List out the methods used to find the HCF of 28 and 56.
The methods used to find the HCF of 28 and 56 are as follows:
Prime Factorisation
Long Division method
Listing common factors
What is the LCM if the HCF of 28 and 56 is 28?
We know that
HCF × LCM = 28 × 56
Given
HCF = 28
28 × LCM = 28 × 56
LCM = 56
Therefore, the LCM is 56
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